Equations and Algebra Notes, Study notes of Mathematics

These are preliminary notes for the topic of Equations and Algebra in Maths.

Typology: Study notes

2022/2023

Uploaded on 04/24/2023

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E q u a t i o n s w i t h v a r i a b l e s o n b o t h s i d e s :
For equations with variables on both sides we can only use the balancing method
We have to perform operations to move -
All the variables to one side of the equation
All the numbers to the other side of the equation
Ex.
E q u a t i o n s w i t h b r a c k e t s :
For equations with brackets (grouping symbols), expand the expression then solve as
usual
Eg.
S i m p l e q u a d r a t i c e q u a t i o n s :
An equation involving a pronumeral squared, such as
𝑥
= 25,
is called a quadratic
equation.
We are doing simple quadratic equations of the type x^2=c (where c is a number)
Ex.
Chapter 10: Equations & Algebra.
Tuesday, 12 October 2021
5:38 PM
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E q u a t i o n s w i t h v a r i a b l e s o n b o t h s i d e s :

  • For equations with variables on both sides we can only use the balancing method We have to perform operations to move - ○ All the variables to one side of the equation ○ All the numbers to the other side of the equation

Ex. E q u a t i o n s w i t h b r a c k e t s : For equations with brackets (grouping symbols), expand the expression then solve as usual Eg. □ 2(3x-4)= □ 6x - 8 = 20 □ 6x = 28 □ X = 4.6666..... (4.67 - 2d.p.)

S i m p l e q u a d r a t i c e q u a t i o n s : An equation involving a pronumeral squared, such as 𝑥ଶ^ = 25 , is called a quadratic equation.

  • We are doing simple quadratic equations of the type x^2=c (where c is a number) Ex.

Chapter 10: Equations & Algebra.

Tuesday, 12 October 2021 5:38 PM

The symbol ±means that

the answer can be both positive or negative on the number line.

E q u a t i o n p r o b l e m s :

  • To solve word problems that require an equation to be solved, you have to create a formula/numerical equation for it using these steps: ○ Choose your pronumeral ○ Translate the words into an equation (tip: underline what's important to make it easier) ○ Solve the equation ○ Use the (therefore) ∴ symbol and write a worded answer for the equation